the air pressure at stations at higher elevation than sea level, such as Laramie

Question

the air pressure at stations at higher elevation than sea level, such as Laramie, WY, needs to be converted to sea level pressure. imagine that the air pressure p at the Laramie airport (elevation z= 2222m) is measured at 777 mbar. what is the corresponding pressure, at sea level? use the following formula: Psl=pe ^(z/H) where Psl is the sea level pressure, H is a constant scale height (H=7800m). Then determine the altitude where the air pressure is 50% of the value at sea level. please show work and explain.

(d) The air pressure at stations at higher elevation than sea level, such as Laramie WY converted to sea level pressure. Imagine that the air pressure p at the Laramie airport (elevation z 2222 m) is measured at 777 mbar. I) What is the corresponding pressure at sea level? Use the following formula: pst peem) where pa is the sea level pressure, H is a constant scale height (H 7800 m). 2) Determine the altitude where the air pressure is 50% of the value at sea level. Hint: taking natural logarithm, In, of psi-pel ) obtain ln(pa) In(p)+Z/H (using the following formulas: In(e)-x and In(xy)-In(x)+In(y) and then derive the formula to calculate Z (using simple algebra!).

Explanation / Answer

A. Since Psl = Pe^(z/H)

Putting values Psl=777 mbar

Z=2222 m and H=7800 m

Psl =777e^(2222/7800)mbar = 1033.093mbar =1.033 bar

B. now pressure is 50% of sea level pressure

SO P= (1/2) Psl

Then Psl =(Psl/2)e^(z/7800)

2 = e^(z/7800)

(ln2)7800 = z

Z= 5406.548 m

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